Brewer Frazier
07/16/2023 · High School
\( \int \frac { e ^ { x } d x } { \sqrt { e ^ { x } } - \sqrt { e ^ { x } + 4 } } \)
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Para resolver la integral
\[
\int \frac{e^x \, dx}{\sqrt{e^x} - \sqrt{e^x + 4}},
\]
realizamos el cambio de variable \( u = \sqrt{e^x} \), lo que conduce a la integral
\[
2 \int \frac{u^2 (u + \sqrt{u^2 + 4}) \, du}{-4}.
\]
Esta integral se puede resolver separando en dos partes y utilizando métodos de integración estándar.
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